CN102853760B - Method for calibrating verticality of magnetic shaft of three-shaft magnetic sensor - Google Patents

Abstract

The invention discloses a method for calibrating verticality of a magnetic shaft of a three-shaft magnetic sensor. A three-dimensional magnetic field generator and a nonmagnetic rotary table are adopted, the three-dimensional magnetic field generator and the nonmagnetic rotary table are arranged at first; the magnetic sensor which needs to be calibrated is fixed on the rotary table; a large magnetic field ranging from top to bottom is generated by the magnetic field generator, so that a numeric value measured by the sensor is not zero; the zero position of the rotary table is marked, the angle values of three shafts of the rotary table are recorded, and three shafts of the rotary table are rotated, so that the outputs of a shaft m and a shaft n of the sensor are zero and the angle values of the three shafts of the rotary table are recorded; the three shafts of the rotary table are rotated again, so that the outputs of a shaft m and a shaft n of the sensor are zero and the angle values of the three shafts of the rotary table are recorded; transformation relation between each shaft m, n and p of a coordinate O and each shaft x3y3z3 of the coordinate O3 can be obtained by calculating multiple recorded angle values so as to obtain a calibration result. The method is simple and feasible, high in accuracy and small in errors.

Description

A kind of scaling method of verticality of magnetic shaft of three-shaft magnetic sensor

Technical field

The present invention relates to a kind of scaling method of verticality of magnetic shaft of three-shaft magnetic sensor.

Background technology

The accurately detecting of detection of magnetic field especially low-intensity magnetic field has related to the key areas such as national defense construction, scientific research, commercial production and daily life, as various aspects such as environmental magnetic field monitoring, research on geomagnetic field, diposits of petroleum exploration, magnetic material nondestructive examination, the investigation of underwater surface Ship-weapon, cosmic space magnetic-field measurements.Want to carry out accurately detecting to magnetic field, the research of magnetic survey method and magnetic survey instrument is crucial.

Magnetic field sensor is one of Primary Component of electronic surveying field and development High-level control system, and the Magnetic Sensor using magnetic material to make and related device are widely used in fields such as Electric Machine Control, industrial robot, medical electronics, robotizations.And along with the development of earth-magnetic navigation technology and other infotecies, people propose more and more higher requirement to the size of Magnetic Sensor, sensitivity, stability and power consumption etc., for this reason, be all devoted to develop the New-type magnet sensors with high sensitivity, fast response and strong anti-interference ability both at home and abroad.

Over nearly twenty or thirty year, magnetic method magnetometer also uses at present in certain field, but its progressively replace by the magnetometer of other forms such as flux-gate magnetometer; Magnetic induction method magnetometer is the most effective impulse magnetic field surveying instrument; Flux-gate magnetometer is widely used, and particularly in the measurement of low-intensity magnetic field, and microminiaturization is the trend of its progress; The discovery of new effect and application, and the appearance of new material and new technology, the range of application of galvanomagnetic effect method magnetometer is expanded further, and particularly giant magnetoresistance, giant magnetoresistance effect method have shown huge application potential in weak magnetic fields measurement field; Magnetic resonance magnetometer, as accurate magnetometer, still occupies critical role in weak magnetic measurement field; Superconductivity effects method magnetometer remains the most accurate magnetic field measuring instrument, and along with the maturation of high temperature SQUID technology, its range of application will expand further; Fibre optic magnetic field surveying instrument based on magneto-optic effect method is suitable for measuring high-intensity magnetic field, but along with the progress of the fiber optic weak magnetic field sensing technology based on magnetostrictive effect, fibre optic magnetic field surveying instrument also will have new application space in weak magnetic fields measurement field.Along with the development of technology and the appearance of new material and new technology such as computing machine, robotization, VLSI (very large scale integrated circuit) manufactures, as Other Instruments, pin-point accuracy, high stability, high resolving power, microminaturization, digitizing, intellectuality are the inevitable directions of magnetic field measurement technology and Instrument Development.

At present, the sensor being applied to static magnetic field measurement is more, wherein the application of triaxial fluxgate magnetometer is comparatively extensive, as geomagnetic field measuring, magnetic detection station in naval vessels magnetic-field measurement, earth-magnetic navigation magnetic-field measurement, to fix a point the occasions such as detection of magnetic field, metal detection, magnetic flaw detection under water.

Triaxial fluxgate magnetometer is instrument conventional in ship's magnetism measurement, geomagnetic field measuring, underawater ordnance fuse and ship navigation.This sensor internal is by three solenoids as its sensitive element to three-dimensional magnetic field, and these three solenoids determine an orthogonal surving coordinate system.But due to reasons such as processing technologys, make such coordinate system determined by three solenoids there is the not exclusively orthogonal systematic error brought of coordinate system three coordinate axis

Three axis magnetometer and three axle Helmholtz coilss all require orthogonal, but due to the restriction of processing technology level and mounting process level, they can not accomplish completely vertical, this nonorthogonality is very outstanding on the impact of whole system precision, so we need measure their verticality and correct.The method of the nonopiate error of perpendicularity of current measurement three axle has, the precision that these methods have is not high, what have is too harsh to equipment requirement, also has the restriction of surveying instrument range, also there is no a kind of good method addressed these problems at present, importantly also there is no a kind of method that three axis magnetometer magnetic axis verticality is demarcated.

Summary of the invention

The present invention is directed to the drawback of the nonopiate error of perpendicularity method of current three axle, propose a kind of three axis magnetometer magnetic axis verticality scaling method that can realize high precision, not limit, be not subject to produce magnetic field accuracy limitations by surveying instrument range.

The technology used in the present invention is as follows:

The present invention adopts three-dimensional magnetic field generator and without magnetic turntable, this three-dimensional magnetic field generator is made up of three groups of mutually orthogonal helmholtz coils and corresponding program controlled constant current source, program controlled constant current source is controlled by computing machine, produce the electric current that constant or expection accordingly changes, thus at the local space that three groups of mutually orthogonal helmholtz coil centers are specified, produce expection, controlled three-dimensional magnetic field, method is: first install three-dimensional magnetic field generator with without magnetic turntable, and needing the Magnetic Sensor demarcated to be fixed on turntable, a large magnetic field is from top to bottom provided by three-dimensional magnetic field generator, Magnetic Sensor is made to be in magnetic field, this magnetic field size is much larger than environmental magnetic field, sensor is respectively measured numerical value that axle records this magnetic-field component is not 0 be full scale, to improve the sensitivity of zero passage and to eliminate the impact of environmental magnetic field, each coordinate system is defined as follows: choosing inertial coordinate is outer shroud coordinate system O ₀-x ₀y ₀z ₀: true origin O ₀on the rotation center of turntable, z ₀axle points to the vertical direction of field generator for magnetic, parallel with the magnetic direction that vertical direction produces, x ₀it is parallel that axle points to horizontal direction and field generator for magnetic direction producing horizontal magnetic field, y ₀axle and x ₀axle, z ₀axle becomes right hand orthogonal coordinate system.Choose without magnetic turntable original state, define outer annulate shaft and point to x ₀direction of principal axis, middle annulate shaft point to y ₀direction of principal axis, inner axle point to z ₀state during direction of principal axis is turntable original state.Choose cyclic coordinate system O in being connected with middle ring framework ₁-x ₁y ₁z ₁: true origin O ₁on the rotation center of turntable, initial time and O ₀-x ₀y ₀z ₀overlap.Choose the inner ring coordinate system O be connected with inner ring framework ₂-x ₂y ₂z ₂: true origin O ₂on the rotation center without magnetic turntable, initial time and O ₁-x ₁y ₁z ₁overlap.Choose the target-based coordinate system O be connected with jig frame ₃-x ₃y ₃z ₃: true origin O ₃on the rotation center without magnetic turntable, initial time and O ₂-x ₂y ₂z ₂overlap.Choose nonopiate magnetic axis coordinate system O-mn p, true origin O is on the rotation center without magnetic turntable, and m, n, p are respectively the true directions of magnetic sensor three magnetic axises.

By given z ₀the externally-applied magnetic field in direction, rotates 3 axles without magnetic turntable, makes sensor, and it is 0 that m, n axle exports, and record is without magnetic turntable 3 shaft angle angle value; Rotate 3 axles without magnetic turntable again, it is 0 that sensor m, p axle is exported, record turntable 3 shaft angle angle value; Continue 3 axles of revolving-turret, it is 0 that sensor n, p axle is exported, record turntable 3 shaft angle angle value.The each axial unit vector om of O-mn p is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₁, r ₂₁, r ₃₁; On is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₂, r ₂₂, r ₃₂; Op is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₃, r ₂₃, r ₃₃.

Then have:

$r_{11}^2+r_{21}^2+r_{31}^2=1---\left(1\right)$

$r_{12}^2+r_{22}^2+r_{32}^2=1---\left(2\right)$

$r_{13}^2+r_{23}^2+r_{33}^2=1---\left(3\right)$

And from O-m n p to O ₃-x ₃y ₃z ₃coordinate be transformed to:

$R_T^3=\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]---\left(4\right)$

From O ₃-x ₃y ₃z ₃to O ₂-x ₂y ₂z ₂coordinate be transformed to:

$R_3^2=\left[\begin{array}{ccc}\cos \mathrm{\γ}& -\sin \mathrm{\γ}& 0\\ \sin \mathrm{\γ}& \cos \mathrm{\γ}& 0\\ 0& 0& 1\end{array}\right]---\left(5\right)$

From O ₂-x ₂y ₂z ₂to O ₁-x ₁y ₁z ₁coordinate be transformed to:

$R_2^1=\left[\begin{array}{ccc}\cos \mathrm{\β}& 0& \sin \mathrm{\β}\\ 0& 1& 0\\ -\sin \mathrm{\β}& 0& \cos \mathrm{\β}\end{array}\right]---\left(6\right)$

From O ₁-x ₁y ₁z ₁to O ₀-x ₀y ₀z ₀coordinate be transformed to:

$R_1^0=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\α}& -\sin \mathrm{\α}\\ 0& \sin \mathrm{\α}& \cos \mathrm{\α}\end{array}\right]---\left(7\right)$

From O-m n p to O ₀-x ₀y ₀z ₀coordinate be transformed to:

⁰R _T＝ ⁰R ₁ ¹R ₂ ²R ₃ ³R _T(8)

Wherein:

α be from original state to final state turntable the angle that turns over of annulate shaft, test the angle turned over three times and be respectively α ₁, α ₂, α ₃; β be from original state to final state turntable the angle that turns over of annulate shaft, test the angle turned over three times and be respectively β ₁, β ₂, β ₃; γ is the angle turned over to final state turntable inner axle from original state, tests the angle turned over three times and is respectively γ ₁, γ ₂, γ ₃.Corresponding to the anglec of rotation of three tests, three tests are from O-mnp to O ₀-x ₀y ₀z ₀coordinate transform be respectively ⁰r _t1, ⁰r _t2, ⁰r _t3.

Note applied field strengths is H, and under final state, externally-applied magnetic field is respectively h along the axial magnetic-field component of Magnetic Sensor three _m, h _n, h _p.

Then have:

$\left[\begin{array}{c}0\\ 0\\ H\end{array}\right]=R_{T1}^0\left[\begin{array}{c}0\\ 0\\ h_p\end{array}\right]---\left(9\right)$

$\left[\begin{array}{c}0\\ 0\\ H\end{array}\right]=R_{T2}^0\left[\begin{array}{c}0\\ h_n\\ 0\end{array}\right]---\left(10\right)$

$\left[\begin{array}{c}0\\ 0\\ H\end{array}\right]=R_{T3}^0\left[\begin{array}{c}{h}_m\\ 0\\ 0\end{array}\right]---\left(11\right)$

Can be obtained by (9):

cosβ ₁cosγ ₁r ₁₃-cosβ ₁sinγ ₁r ₂₃+sinβ ₁r ₃₃＝0 (12)

(sinα ₁sinβ ₁cosγ ₁+cosα ₁sinγ ₁)r ₁₃+(-sinα ₁sinβ ₁sinγ ₁+cosα ₁cosγ ₁)r ₂₃-sinα ₁cosβ ₁r ₃₃＝0(13)

Can be obtained by (10):

cosβ ₂cosγ ₂r ₁₂-cosβ ₂sinγ ₂r ₂₂+sinβ ₂r ₃₂＝0 (14)

(sinα ₂sinβ ₂cosγ ₂+cosα ₂sinγ ₂)r ₁₂+(-sinα ₂sinβ ₂sinγ ₂+cosα ₂cosγ ₂)r ₂₂-sinα ₂cosβ ₂r ₃₂＝0(15)

Can be obtained by (11):

cosβ ₃cosγ ₃r ₁₁-cosβ ₃sinγ ₃r ₂₁+sinβ ₃r ₃₁＝0 (16)

(sinα ₃sinβ ₃cosγ ₃+cosα ₃sinγ ₃)r ₁₁+(-sinα ₃sinβ ₃sinγ ₃+cosα ₃cosγ ₃)r ₂₁-sinα ₃cosβ ₃r ₃₁＝0(17)

Solution is by equation (1)-(3), and the homogeneous equation group that equation (12)-(17) form, can solve ³r _t, namely sensor three magnetic axises are relative to the calibration matrix of sensor fixed coordinate system.

The inventive method simple possible, precision is high, and the verticality adopting zero passage method to demarcate magnetic shaft of three-shaft magnetic sensor does not rely on the range of sensor, is applicable to the sensor of any range.Do not rely on other magnetic field measuring instrument, the measuring error of other magnetic field measuring instrument can not be brought.Be measured as static measurement, can not dynamic measurement error be brought.What demarcate is angle between true magnetic axis, and Magnetic Sensor can not be brought to measure error between axle and true magnetic axis.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is three-axle table schematic diagram;

Embodiment

Native system adopts without magnetic turntable and three-dimensional magnetic field generator.

Three-dimensional magnetic field generator, is made up of three groups of mutually orthogonal helmholtz coils and corresponding program controlled constant current source.Program controlled constant current source is controlled by computing machine, can produce the electric current of constant or expection change accordingly, thus at the local space that three groups of mutually orthogonal helmholtz coil centers are specified, produce expection, controlled three-dimensional magnetic field.The scaling method of verticality of magnetic shaft of three-shaft magnetic sensor is: first install three-dimensional magnetic field generator with without magnetic turntable, and needing the Magnetic Sensor demarcated to be fixed on turntable.A large magnetic field is from top to bottom provided by magnetic field generator, Magnetic Sensor is made to be in magnetic field, this magnetic field size is much larger than environmental magnetic field, make sensor magnetic axis and Calibration Field once out of plumb, the numerical value that magnetic axis records will exceed range, to improve the sensitivity of zero passage and to eliminate the impact of environmental magnetic field.If weak magnetic sensor, the situation that the impact of environmental magnetic field cannot be ignored, then need a magnetic shield room, create a non-magnetic environment, calibration facility is arranged in magnetic shield room.Coordinate system is defined as follows: choosing inertial coordinate is outer shroud coordinate system O ₀-x ₀y ₀z ₀: true origin O ₀on the rotation center of turntable, z ₀axle points to the vertical direction of field generator for magnetic, parallel with the magnetic direction that vertical direction produces, x ₀the horizontal direction that axle points to field generator for magnetic is parallel with the magnetic direction that a horizontal direction produces, y ₀axle and x ₀axle, z ₀axle becomes right hand orthogonal coordinate system, chooses turntable original state, defines outer annulate shaft and points to x ₀direction of principal axis, middle annulate shaft point to y ₀direction of principal axis, inner axle point to z ₀state during direction of principal axis is turntable original state, chooses cyclic coordinate system O in being connected with middle ring framework ₁-x ₁y ₁z ₁: true origin O ₁on the rotation center of turntable, initial time and O ₀-x ₀y ₀z ₀overlap, choose the inner ring coordinate system O be connected with inner ring framework ₂-x ₂y ₂z ₂: true origin O ₂on the rotation center of turntable, initial time and O ₁-x ₁y ₁z ₁overlap, choose the target-based coordinate system O be connected with jig frame ₃-x ₃y ₃z ₃: true origin O ₃on the rotation center of turntable, initial time and O ₂-x ₂y ₂z ₂overlap, choose nonopiate magnetic axis coordinate system O-mn p, true origin O is on the rotation center of turntable, and m, n, p are respectively the true directions of magnetic sensor three magnetic axises;

By given z ₀the externally-applied magnetic field in direction, 3 axles of revolving-turret, make sensor, and it is 0 that m, n axle exports, record turntable 3 shaft angle angle value; 3 axles of revolving-turret again, it is 0 that sensor m, p axle is exported, record turntable 3 shaft angle angle value; Continue 3 axles of revolving-turret, it is 0 that sensor n, p axle is exported, and record turntable 3 shaft angle angle value, each axial unit vector om of O-mn p is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₁, r ₂₁, r ₃₁; On is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₂, r ₂₂, r ₃₂; Op is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₃, r ₂₃, r ₃₃;

Then have:

$r_{11}^2+r_{21}^2+r_{31}^2=1---\left(1\right)$

$r_{12}^2+r_{22}^2+r_{32}^2=1---\left(2\right)$

$r_{13}^2+r_{23}^2+r_{33}^2=1---\left(3\right)$

And from O-mn p to O ₃-x ₃y ₃z ₃coordinate be transformed to:

$R_T^3=\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]---\left(4\right)$

From O ₃-x ₃y ₃z ₃to O ₂-x ₂y ₂z ₂coordinate be transformed to:

$R_3^2=\left[\begin{array}{ccc}\cos \mathrm{\γ}& -\sin \mathrm{\γ}& 0\\ \sin \mathrm{\γ}& \cos \mathrm{\γ}& 0\\ 0& 0& 1\end{array}\right]---\left(5\right)$

From O ₂-x ₂y ₂z ₂to O ₁-x ₁y ₁z ₁coordinate be transformed to:

$R_2^1=\left[\begin{array}{ccc}\cos \mathrm{\β}& 0& \sin \mathrm{\β}\\ 0& 1& 0\\ -\sin \mathrm{\β}& 0& \cos \mathrm{\β}\end{array}\right]---\left(6\right)$

From O ₁-x ₁y ₁z ₁to O ₀-x ₀y ₀z ₀coordinate be transformed to:

$R_1^0=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\α}& -\sin \mathrm{\α}\\ 0& \sin \mathrm{\α}& \cos \mathrm{\α}\end{array}\right]---\left(7\right)$

From O-mn p to O ₀-x ₀y ₀z ₀coordinate be transformed to:

⁰R _T＝ ⁰R ₁ ¹R ₂ ²R ₃ ³R _T(8)

Wherein,

α be from original state to final state turntable the angle that turns over of annulate shaft, test the angle turned over three times and be respectively α ₁, α ₂, α ₃;

β be from original state to final state turntable the angle that turns over of annulate shaft, test the angle turned over three times and be respectively β ₁, β ₂, β ₃;

γ is the angle turned over to final state turntable inner axle from original state, tests the angle turned over three times and is respectively γ ₁, γ ₂, γ ₃;

Corresponding to the anglec of rotation of three tests, three tests are from O-mnp to O ₀-x ₀y ₀z ₀coordinate transform be respectively ⁰r _t1, ⁰r _t2, ⁰r _t3;

Note applied field strengths is H, and under final state, externally-applied magnetic field is respectively h along the axial magnetic-field component of Magnetic Sensor three _m, h _n, h _p,

Then have:

$\left[\begin{array}{c}0\\ 0\\ H\end{array}\right]=R_{T1}^0\left[\begin{array}{c}0\\ 0\\ h_p\end{array}\right]---\left(9\right)$

$\left[\begin{array}{c}0\\ 0\\ H\end{array}\right]=R_{T2}^0\left[\begin{array}{c}0\\ h_n\\ 0\end{array}\right]---\left(10\right)$

$\left[\begin{array}{c}0\\ 0\\ H\end{array}\right]=R_{T3}^0\left[\begin{array}{c}{h}_m\\ 0\\ 0\end{array}\right]---\left(11\right)$

Can be obtained by (9):

cosβ ₁cosγ ₁r ₁₃-cosβ ₁sinγ ₁r ₂₃+sinβ ₁r ₃₃＝0 (12)

(sinα ₁sinβ ₁cosγ ₁+cosα ₁sinγ ₁)r ₁₃+(-sinα ₁sinβ ₁sinγ ₁+cosα ₁cosγ ₁)r ₂₃-sinα ₁cosβ ₁r ₃₃＝0(13)

Can be obtained by (10):

cosβ ₂cosγ ₂r ₁₂-cosβ ₂sinγ ₂r ₂₂+sinβ ₂r ₃₂＝0 (14)

(sinα ₂sinβ ₂cosγ ₂+cosα ₂sinγ ₂)r ₁₂+(-sinα ₂sinβ ₂sinγ ₂+cosα ₂cosγ ₂)r ₂₂-sinα ₂cosβ ₂r ₃₂＝0(15)

Can be obtained by (11):

cosβ ₃cosγ ₃r ₁₁-cosβ ₃sinγ ₃r ₂₁+sinβ ₃r ₃₁＝0 (16)

(sinα ₃sinβ ₃cosγ ₃+cosα ₃sinγ ₃)r ₁₁+(-sinα ₃sinβ ₃sinγ ₃+cosα ₃cosγ ₃)r ₂₁-sinα ₃cosβ ₃r ₃₁＝0(17)

Solution is by equation (1)-(3), and the homogeneous equation group that equation (12)-(17) form, can solve ³r _t, namely sensor three magnetic axises are relative to the calibration matrix of sensor fixed coordinate system.

Claims (2)

1. the scaling method of a verticality of magnetic shaft of three-shaft magnetic sensor, adopt three-dimensional magnetic field generator and without magnetic turntable, described three-dimensional magnetic field generator is made up of three groups of mutually orthogonal helmholtz coils and corresponding program controlled constant current source, program controlled constant current source is controlled by computing machine, produce the electric current that constant or expection accordingly changes, thus at the local space that three groups of mutually orthogonal helmholtz coil centers are specified, produce expection, controlled three-dimensional magnetic field, adopt additional fixing large magnetic field, zero position was exported by record sensor, and then carry out calculating nominal data, it is characterized in that, method is as follows:

First install three-dimensional magnetic field generator with without magnetic turntable, and needing the Magnetic Sensor demarcated to be fixed on without on magnetic turntable, a large magnetic field is from top to bottom provided by three-dimensional magnetic field generator, Magnetic Sensor is made to be in magnetic field, this magnetic field size is much larger than environmental magnetic field, the numerical value making Magnetic Sensor respectively measure this magnetic-field component that axle records is not 0 be full scale, to improve the sensitivity of zero passage and to eliminate the impact of environmental magnetic field;

Coordinate system is defined as follows: choosing inertial coordinate is outer shroud coordinate system O ₀-x ₀y ₀z ₀: true origin O ₀on the rotation center without magnetic turntable, z ₀axle points to the vertical direction of helmholtz coil, parallel with the magnetic direction that vertical direction produces, x ₀it is parallel that axle points to horizontal direction and helmholtz coil direction producing horizontal magnetic field, y ₀axle and x ₀axle, z ₀axle becomes right hand orthogonal coordinate system, chooses without magnetic turntable original state, defines outer annulate shaft and points to x ₀direction of principal axis, middle annulate shaft point to y ₀direction of principal axis, inner axle point to z ₀state during direction of principal axis is without magnetic turntable original state, chooses cyclic coordinate system O in being connected with middle ring framework ₁-x ₁y ₁z ₁: true origin O ₁on the rotation center without magnetic turntable, initial time and O ₀-x ₀y ₀z ₀overlap; Choose the inner ring coordinate system O be connected with inner ring framework ₂-x ₂y ₂z ₂: true origin O ₂on the rotation center without magnetic turntable, initial time and O ₁-x ₁y ₁z ₁overlap; Choose the target-based coordinate system O be connected with jig frame ₃-x ₃y ₃z ₃: true origin O ₃on the rotation center without magnetic turntable, initial time and O ₂-x ₂y ₂z ₂overlap; Choose nonopiate magnetic axis coordinate system O-m n p, true origin O is on the rotation center without magnetic turntable, and m, n, p are respectively the true directions of magnetic sensor three magnetic axises;

By given z ₀the externally-applied magnetic field in direction, rotates 3 axles without magnetic turntable, and it is 0 that sensor m, n axle is exported, and record is without magnetic turntable 3 shaft angle angle value; Rotate 3 axles without magnetic turntable again, it is 0 that sensor m, p axle is exported, and record is without magnetic turntable 3 shaft angle angle value; Continue to rotate 3 axles without magnetic turntable, it is 0 that sensor n, p axle is exported, and record is without magnetic turntable 3 shaft angle angle value, and each axial unit vector om of O-m n p is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₁, r ₂₁, r ₃₁; On is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₂, r ₂₂, r ₃₂; Op is at O ₃-x ₃y ₃z ₃in coordinate be r ₁₃, r ₂₃, r ₃₃;

Then have:

And from O-mn p to O ₃-x ₃y ₃z ₃coordinate be transformed to:

From O ₃-x ₃y ₃z ₃to O ₂-x ₂y ₂z ₂coordinate be transformed to:

From O ₂-x ₂y ₂z ₂to O ₁-x ₁y ₁z ₁coordinate be transformed to:

From O ₁-x ₁y ₁z ₁to O ₀-x ₀y ₀z ₀coordinate be transformed to:

From O-mn p to O ₀-x ₀y ₀z ₀coordinate be transformed to:

⁰R _T＝ ⁰R ₁ ¹R ₂ ²R ₃ ³R _T(8)

Wherein:

α is that the angle that three tests turn over is respectively α without the angle that the outer annulate shaft of magnetic turntable turns over from original state to final state ₁, α ₂, α ₃;

β is without the angle that annulate shaft in magnetic turntable turns over from original state to final state, tests the angle turned over three times and is respectively β ₁, β ₂, β ₃;

γ is without the angle that magnetic turntable inner axle turns over from original state to final state, tests the angle turned over three times and is respectively γ ₁, γ ₂, γ ₃;

Corresponding to the anglec of rotation of three tests, three tests are from O-mn p to O ₀-x ₀y ₀z ₀coordinate transform be respectively ⁰r _t1, ⁰r _t2, ⁰r _t3;

Note applied field strengths is H, and under final state, externally-applied magnetic field is respectively h along the axial magnetic-field component of Magnetic Sensor three _m, h _n, h _p, then have:

Obtained by (9):

cosβ ₁cosγ ₁r ₁₃-cosβ ₁sinγ ₁r ₂₃+sinβ ₁r ₃₃＝0 (12)

(sinα ₁sinβ ₁cosγ ₁+cosα ₁sinγ ₁)r ₁₃+(-sinα ₁sinβ ₁sinγ ₁+cosα ₁cosγ ₁)r ₂₃-sinα ₁cosβ ₁r ₃₃＝0 (13)

Obtained by (10):

cosβ ₂cosγ ₂r ₁₂-cosβ ₂sinγ ₂r ₂₂+sinβ ₂r ₃₂＝0 (14)

(sinα ₂sinβ ₂cosγ ₂+cosα ₂sinγ ₂)r ₁₂+(-sinα ₂sinβ ₂sinγ ₂+cosα ₂cosγ ₂)r ₂₂-sinα ₂cosβ ₂r ₃₂＝0 (15)

Obtained by (11):

cosβ ₃cosγ ₃r ₁₁-cosβ ₃sinγ ₃r ₂₁+sinβ ₃r ₃₁＝0 (16)

(sinα ₃sinβ ₃cosγ ₃+cosα ₃sinγ ₃)r ₁₁+(-sinα ₃sinβ ₃sinγ ₃+cosα ₃cosγ ₃)r ₂₁-sinα ₃cosβ ₃r ₃₁＝0 (17)

Solution is by equation (1)-(3), and the homogeneous equation group that equation (12)-(17) form, can solve ³r _t, namely sensor three magnetic axises are relative to the calibration matrix of target-based coordinate system.

2. the scaling method of a kind of verticality of magnetic shaft of three-shaft magnetic sensor according to claim 1, it is characterized in that: the Magnetic Sensor that needs are demarcated, when the impact of environmental magnetic field cannot be ignored, then need a magnetic shield room, three-dimensional magnetic field generator and being arranged in magnetic shield room without magnetic turntable.